Question: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{r^2 - 8r}{r^2 - 16r + 64}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{r^2 - 8r}{r^2 - 16r + 64} = \dfrac{(r)(r - 8)}{(r - 8)(r - 8)} $ Notice that the term $(r - 8)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r - 8)$ gives: $p = \dfrac{r}{r - 8}$ Since we divided by $(r - 8)$, $r \neq 8$. $p = \dfrac{r}{r - 8}; \space r \neq 8$